A novel experimental approach involving fluorescence nonradiative energy transfer (NRET) is employed to study the Fickian diffusion of small molecules in rubbery polymer films near the glass transition. A theoretical formalism has been developed which directly relates the small molecule translational diffusion coefficient, gamma, to changes in the energy transfer efficiency, E. Values of gamma, as low as 5 x 10(-16) cm(2)/s have been measured. In this approach, two thin polymer films are sandwiched together, one labeled with either NRET donor or acceptor chromophores and the second doped with the complementary chromophore. Upon annealing for a time t, dopant chromophore diffusion occurs in which E is proportional to (gamma/t)(1/2)/omega, where omega is the donor film thickness. Values of gamma for pyrene, N-(2-hydroxyethyl)-N-ethyl-4-(tricyanovinyl)aniline (TC1), bis(phenylethynylanthracene) (BPEA), and decacyclene in poly(isobutyl methacrylate) (PiBMA) and for BPEA in poly(ethyl methacrylate) (PEMA) have been measured over temperatures ranging from ca. T-g to T-g + 20 degrees C. Among these chromophores, significant differences in both the magnitude and temperature dependence of gamma were observed and are attributed to differences in molecule size, shape, and flexibility. Two anomalous effects are observed from a comparison of translational diffusion and rotational reorientation dynamics of TC1 in PiBMA near T-g. The first is an apparent enhancement in translational diffusion relative to rotational reorientation dynamics, with the average translational displacement of a chromophore during an average rotational relaxation time, , being a couple orders of magnitude larger than the length of the molecule. This behavior may be explained by significant local-scale heterogeneity in the polymer, i.e., the broad distribution of polymer alpha-relaxation times. The second regards the different temperature dependencies of and gamma near T-g. This may be explained qualitatively by a strong temperature dependence of the breadth of the distribution of a-relaxation times, an effect known to be present in the TC1-PiBMA system employed in this comparison as well as a variety of other polymer systems near T-g.